1. Field of The Invention
This invention relates to a system for representing musical tone information used in an electronic musical instrument, and more particularly, to an improvement in the processing of quantities or operands used in an operational expression representing the musical tone information.
2. Description of the Related Art
In conventional electronic musical instruments, musical tone information, for example, information on amplitude levels of a signal representing a musical tone, is obtained by first determining or selecting the waveform of the musical tone and then multiplying the magnitude of the voltage of a signal indicating the musical tone having the determined or selected waveform at each moment by a corresponding level of an envelope, or adding a level of an envelope to the magnitude at the voltage of a signal indicating the musical tone having the determined or selected waveforms at each moment. Further, the magnitude of the voltage of the musical tone is represented by a large number of discrete levels in the electronic musical instrument. Therefore, to represent a smaller change in magnitude in voltage of the signal by increasing the number of discrete levels (i.e., by making the interval between two contiguous levels smaller), it is necessary to increase the number of bits used for representing the data (hereunder referred to as waveform data and envelope data) representing the waveform and the envelope, and therefore, the number of bits required for representing the result of the multiplication of the waveform data and the envelope data is also increased. Accordingly, a multiplying circuit or multiplier able to process data represented by a large number of bits becomes necessary.
Noted, the value [EN] of the envelope data EN and the value [W] of the waveform data W can be represented in the following forms. ##EQU1##
Therefore, the result [RM] of the multiplication of the envelope data EN and the waveform data W is expressed as follows. ##EQU2##
As understood from equation (3), the result [RM] can be computed by first effecting the addition of the exponents. Note, the multiplicand (2.sup.(Pa+Pw)) and the multiplicator or multiplier (2.sup.(Ma+Mw)) will be sometimes referred to hereafter as a power data and a mantissa data respectively. Further, the multiplicators 2.sup.Ma, 2.sup.Mw and 2.sup.(Ma+Mw) in the expressions (1) and (2) are similar to or correspond to a mantissa when using a well-known floating-point representation of data, and therefore, the exponent (for example, Ma, Mw or (Ma+Mw)) of a multiplicator will be sometimes referred to hereafter as the mantissa part data. Moreover, the exponents Pa, Pw and (Pa+Pw) of the multiplicand 2.sup.Pa, 2.sup.Pw, or 2.sup.(Pa+Pw) in the expressions (1) and (2) are similar to or correspond to, a power in case of using well-known floating-point representation of data, and thus the exponent (for example, Pa, Pw or (Pa+Pw)) of a multiplicand will be sometimes referred to hereafter as the power part data.
Where the musical tone information or data is represented by using the above-described expression, it is preferable to obtain a dynamic range in which the maximum absolute value of a decibel is around 90 dB-96 dB.
Further, when using a first conventional type expression given basically by the following equation: ##EQU3## the relation ship between the power part data P and the decibel is listed below. Note, the notation "X" will be used hereafter to indicate that X is a binary number. ##EQU4## In this case, as many as 5 bits are required for representing the power part data P corresponding to around -90 dB.
Next, when using a second conventional type expression given basically by the following equation: ##EQU5## the relation ship among the power part data P, the quantity P' (=-P), and the decibel is as listed below. ##EQU6##
Therefore, in this case, although only 4 bits are required for representing the power part data P, around -90 dB can be achieved, but this second conventional type expression has encountered the problem as described hereafter.
Namely, when performing the following operation ##EQU7## if the exponent (Ma.times.Mw) is equal to or larger than 1, a carry operation must be performed as expressed in the following equations. ##EQU8##
Namely, the power part data P is not incremented by 1 but decremented by 1, due to the carry generated in the mantissa part data M, and accordingly, when using the second conventional type expression, the calculation of the mantissa part data M must be made separately from that of the power part data P.
The present invention is intended to solve the problem of the conventional system.
Therefore an object of the present invention is to provide an improved system in which the carry operation can be easily and simply performed when a carry is generated in the mantissa M.